The monodromy of meromorphic projective structures

Allegretti, Dylan; Bridgeland, Tom

doi:10.1090/tran/8093

The monodromy of meromorphic projective structures
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by Dylan G. L. Allegretti and Tom Bridgeland PDF

Trans. Amer. Math. Soc. 373 (2020), 6321-6367 Request permission

Abstract:

We study projective structures on a surface having poles of prescribed orders. We obtain a monodromy map from a complex manifold parameterising such structures to the stack of framed $\operatorname {PGL}_2(\mathbb {C})$ local systems on the associated marked bordered surface. We prove that the image of this map is contained in the union of the domains of the cluster charts. We discuss a number of open questions concerning this monodromy map.

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